UNCLASSIFIED AD NUMBER AD826735 NEW LIMITATION CHANGE TO Approved for public release, distribution unlimited FROM Distribution authorized to U.S. Gov't. agencies and their contractors; Administrative/Operational Use; Nov 1967. Other requests shall be referred to US Army Ballistic Research Lab., Aberdeen Proving Ground, MD. AUTHORITY Army Armament R&D Ctr, Aberdeen Proving Ground, MD ltr dtd 20 Feb 1981 THIS PAGE IS UNCLASSIFIED 14A REPORT NO. 1371 THE PRODUCTION OF FIRING TABLES FOR CANNON ARTILLERY 030 by let Elizabeth R. Dickinson November 1967 This document is subject to special export controls and each transmittal to foreign governments or foreign nationals may be made only with prior approval of Commanding Officer, U.S. Army Ballistic Research Laboratories, Aberdeen Proving Ground, Maryland U. S. ARMY MATERIEL COMMAND BALLISTIC RESEARCH LABORATORIES ABERDEEN PROVING GROUND, MARYLANP Destroy this report when it is no longer needed. Do not return it to the originator. .... .... .. i The findings in this report are not to be construed as an official Department of the Army position, unless so designated by other authorized documents. SBALLISTIC RESEARCG1 LAbUKA OIURES REPORT NO. 1371 NOVEMBER 1967 THE PRODUCTION OF FIRING TABLES FOR CANNON ARTILLERY Elizabeth R. Dickinson Computing Laboratory This document Is subject to special export controls and each transmittal to foreign governments or foreign nationals may be made only with prior Sarpoval of Commanding Officer, U.S. Army Ballistic Research Laboratories, Aerdan Proving Ground, Maryland RDT&E Project No. 1T523801A287 ABERDEEN P ROVING GROUND, MARYLAND I BALLISTIC RESEARCH LABORATORIES REPORT NO. 1371 ERDickinson/sw Aberdeen Proving Ground, Md. November 1967 I THE PRODUCTION OF FIRING TABLES I FOR CANNON ARTILLERY SABSTRACT This report describes in detail the acquisition and analysis of firing data as well as the conversion of the measured data to printed firing tables. I, 3 3. TABLE OF CONTENTS ABSTRACT....................................... ...... 3 I. TABLE OF SYMBOLS AND ABBREVIATIONS ......... ... ............ 7 II. INTRODUCTION ....... ....... ...................... .. 10 III. REQUIREMENT FOR A FIRING TABLE ................... ........ 11 IV. ACQUISITION OF DATA FOR A FIRING TABLE ....... ...... .... 12 A. Data for Velocity Zoning ....... ........... ......... 12 B. Data for Provisional Table ..... ..... ........ ..... 15 C. Data for Final Table ..... ... ..... 16 V. ANALYSIS OF RAW DATA ............... ..... 21 A. Equations of Motion . 21 B. Drag Coefficient . ...... 23 C. Reduction of Range Firing Data ........... 24 1. Preparation for Reduction for Ballistic Coefficient • 24 a. Formation of Points ....... 24 b. Meterological Data . 25 c. Muzzle Velocity . ........ .. 25 d. Means and Probable Errors, per Point . 27 e. N-Factor . 28 f. Change in Velocity for a Change in Propellant Temperature . ........ 31 g. Compensation for Rotation of Earth .. ....... ... 32 2. Reduction for Ballistic Coefficient . ...... 32 a. Ballistic Coefficient and Jump . ....... 32 b. Change in Range for Change in Elevation, Velocity and Ballistic Coefficient . ......... 40 4 I TARBLE O1F rnNTRNTS (Ccntinued) Page c. Drift . 40 II d. Time . 41 3. Probable Errors, per Charge ...... ............ .. 43 a. Probable Error in Range to Impact ..... ....... 43 b. Probable Error in Deflection .... ......... .. 44 4. Fuze Data . .......... 45 a. Fuze Setting . 45 b. Probable Error in Time to Burst . .46 c. Probable Error in Height of Burst and Probable Error in Range to Burst .......... 47 5. Illuminating Projectile . 47 VI. COMPUTATIONS FOR THE TABULAR FIRING TABLE . 50 A. Table A: Line Number . ... 50 B. Table B: Complementary Range and Line Number ..... 55 C. Table C: Wind Components ........ 58 D. Table D: Air Temperature and Density Corrections . 58 E. Table E: Propellant Temperature . 59 F. Table F: Ground Data and Correction Factors . 59 G. Table G1 Supplementary Data ........ ... 62 H. Table H: Rotation (Corrections to Range) .. 64 I. Table I: Rotation (Corrections to Azimuth) . .. 66 J. Table J: Fuze Setting Factors .. ........ .67 K. Table K: AR, AH (Elevation) . ..... 67 L. Table L: &R, AR (Time) ........ ...... 69 M. Table M: Fuze Setting . ..... 70 5 TABLE OF CONTENTS (Continued) r age N. illuminating Projectile ....... ................. ... 70 0. Trajectory Charts ...... ... ...................... 72 VII. PUBLICATION OF THE TABULAR FIRING TABLE ........... 74 VIII. ADDITIONAL AIMING DATA .............. .................... 75 A. Graphical Equipment ........... .................. .. 75 1. Graphical Firing Table . .............. 75 2. Graphical Site Table . ..... ............... 78 3. Wind Cards . 80 4. Graphical Equipment for Illuminating Projectiles . 84 B. Reticles and Aiming Data Charts . .......... 86 REFERENCES . 90 APPENDIX . 93 DISTRIBUTION LIST . I.1 p 6 1. TABLE OF SYMBOLS AND ABBREVIATIONS AC Azimuth correction for wind BRLESC Ballistic Research Laboratories Electronic Scientific Computer C Ballistic coefficient CDC Combat Developments Command CS Complement~ary angle of site D Deflection, drift C F Fork FS Fuze setting PSC Fuze setting correction for wind G G~vre function GFT Graphical firing table GST Graphical site table H "Heavy, height ! ICAO International Civil Aviation Organization J Jump KD Drag coefficientDi L Latitude, lightweight, distance from the trunnion of the gun to the muzzle M Mach number (velocity of projectile/velocity of sound), MDP Meteorological datum plans MPT Mean firing time MLW "Mean low water I. IAaL6 U' SiThiOLS AND ABBREVIATiONS (uUiLiuuud) MRT Mean release time MSL Mean sea level N-Factor Factor for correcting the velocity of a projectile of nonstandard weight PE Probable error QMR Qualitative materiel requirement R Range RC Range correction for wind S Spin T Observed time of flight, target V Velocity VI Vertical interval Wh Headwind W Tailwind W Range wind x W Cross wind z Z Deflection axpay a z Accelerations due to the rotation of the earth d Diameter Sg Acceleration due to gravity h Height of the trunnions of the gun above mean low water n Calibers per revolution, 1/n - twist in revolutions per caliber 8 I I. TABLE OF SYMBOLS AND ABBREVIATIONS (Continued) s Standard deviation t Computed time of flight x Distance along the line of fire y Height z Distance to the right or left of the line of fire of ti.e line of fire SAzimuth S Chart direction of the wind Azimuth of the wind X1,2,3 Components of the earth's angular velocity 0 Angle of elevation, angle of departure p Air density as a function of height Angular velocity of the earth Mil First and second derivatives with respect to time Subscripts o Initial value n Nonstandard value s Standard value W Final value 9 II. INTRODUCTION Ideally, a firing table enables the artilleryman to solve his fire problem and to hit the target with the first round fired. In• the pre- sent state of the art, this goal is seldom achieved, except coinci- 4 dently. The use of one or more forward observers, in conjunction with the use of a firing table, enables the artilleryman to adjust his fire and hit the target with the third or fourth round fired. It is, however, the ultimate goal of the Firing Tables Branch of the Ballistic Research Laboratories (BRL) to give the artilleryman the N-P tool for achieving accurate, predicted fire. This report is concerned with the steps involved in the production ;V of a current artillery firing table. with principal emphasis on the conversion of measured data to printed tables. No report has been published on the computational procedures for producing firing tables since that of Gorn and Juncosa(I)* in 1954. As a new high speed compu- ter, with a much larger memory, the Ballistic Research Laboratories Electronic Scientific Computer (BRLESC), has been added to the compu- ting facilities at BRL, the computation of firing tables has become more highly mechanized than it was in 1954. Ni description has been published of the process by which the necessary data for a firing table are acquired. Thus, the purpose of this report in two-fold: to update the work of Gorn and Juncosa, and to trace the history of a firing table from the adoption of a new weapon or a new piece of anmunition to the publication of a table for the use of that weapon or ammuni.tion in the field. *Superscriptnumbers in pare:itheses denote references which may be found on page 90. 10 III. REQUIREMENT FOR A FTRTNC TARBL Whenever a new combination of artillery weapon and ammunition goes into the field, a firing table must accompany the system. There is a rather lengthy chain of events leading up to the placing in the field of a new weapon or a new projectile. Initially, the requirement for such an item is written by the Combat Developments Command (CDC). The qualitative materiel requirement (QMR) set up by CDC is very detailed, listing weight, lethality, transportability and many other attributes as well as performance characteristics. After the item has passed through the research and development stage, it is subjected to safety, engineering and service tests. When all tests are passed satisfactorily, the item is classified as standard and goes into production. As soon as the production item is available, it and its firing table are released to troops for training. Thus as soon as a QMR is published, it is known that a firing table will be ultimately required. In addition, a provisional firing table will be needed to conduct the firings for the various tests of the item. rI I IV. ACQUISITION OF DATA FOR A FIRING TABLE We acquire data for firing tables in several stages and for several purposes: to provide velocity zoning, to produce a provisional table and to produce a final table. A. Data for Velocity Zoning Velocity zoning can be defined as the establishment of a series of finite weights of propellant, called charges, which are to be used to deliver a projectile, by means of a given weapon system, to certain required ranges. Within each zone, or charge, an infinite variation of elevations permits the gunner to deliver the projectile at any range up to the maximum for that charge. Zoning gives flexibility to a weapon system.